Homework 3.2

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Homework 3.2

1. Fill in the blank to correctly complete the sentence. Consider the following function.

f (x) = 3 x^{4} + 5 x^{3} - 7 x^{2} + 3 x + 13 = (x - 2) (3 x^{3} + 11 x^{2} + 15 x + 33) + 79

2. Divide.

\frac{2 x^{4} - 14 x^{3} + 21 x^{2} - 6 x + 5}{x - 5}

3. Use synthetic division to perform the division.

$\frac{- 6 x^{3} + 8 x^{2} - 5 x + 3}{x - 2}$ $\frac{x^{4} + 2 x^{3} + 3 x^{2} + 7 x + 2}{x + 2}$

4. Use synthetic division to perform the following division.

$\frac{x^{3} - 343}{x - 7}$

5. Use synthetic division to perform the division.

$\frac{x^{5} + 1}{x + 1}$

6. For the following polynomial function, use the remainder theorem to find f(k).

$f (x) = 3 x^{2} - 5 x - 5; k = 4$

$f (4)$

7. Use the remainder theorem and synthetic division to find f(k) for the given value of k.

$f (x) = - x^{3} - 9 x^{2} - 21 x - 6; k = - 5$

$f (- 5) =$

8. Use synthetic division to perform the division.

$\frac{x^{4} + 2 x^{3} + 3 x^{2} + 7 x + 2}{x + 2}$

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This question is taken from Math 260 – PreCalculus » Fall 2021 » Homeworks